# 5.1 The environment the factorization scheme assumes

The environmental clause for this family fixes the domain parameters, the modulus construction, the basic numbers and the trust path by which a verifier learns the claimant parameters. The assumptions are similar to the identity family, but the modulus and the basic numbers carry more of the security.

## What it asks

Evidence the domain parameter distribution, the modulus construction and the basic number selection, and show how a verifier obtains an authentic copy of the claimant parameters. Where the modulus is shared across a domain, record who can use the factors and for what.

## What the revision does

The fourth edition will restate these conditions. The public record does not give the new wording, so the 2009 conditions are the baseline on this page.

## Who it binds

The domain authority, the verifier operator and the key management owner.

## Evidence an auditor samples

- The domain parameter set and its distribution record (cryptography standard)
- The modulus construction record, with factor custody (key management)
- The basic number selection and its justification (design note)
- The authentic claimant parameter path to the verifier (architecture)

## The test you can run

Pick a verifier and trace the claimant parameters back to their source. If the trace ends at a manual copy, the trust path is undocumented.

## Common failures

- The basic numbers are chosen once and never reviewed against the modulus.
- A shared modulus has no record of who may use the factors.

## How to close it

Draw the trust path for one deployment and put a date and an owner on each hop. The drawing is the evidence an assessor will ask for, and it exposes the manual copy that nobody owns.

## Source

ISO/IEC 9798-5:2009(E), 5.1, publisher preview; replaced by ISO/IEC DIS 9798-5, stage 40.20. Read on 21 October 2026. Our wording, not the instrument's.
https://www.iso.org/standard/89516.html

Not legal advice; does not certify.